1. Field of the Invention
This invention relates to a route predicting apparatus, and more particularly to an apparatus adapted to monitor a movement of a flying target to predict a route of the target even when an observed value is temporarily not available due to obstacles such as mountains.
2. Description of the Prior Art
Conventionally, as a route predicting apparatus for such a target, a tracking filter for tracking a target has been used on the assumption that necessary information is obtainable at any time.
FIG. 1 is a schematic block diagram illustrating a tracking filter described in R. A. Singer and K. W. Behnke "Realtime tracking filter evaluation and selection for tactical applications", IEEE TRANS., VOL. AES7, NO. 1 (1971). The tracking filter provided by R. A. Singer utilized a Kalman filter and has been used as a model for subsequent tracking filters. In utilizing such a tracking filter for a route predicting apparatus, the configuration shown in FIG. 1 is used when a target is observable, while it is modified as shown in the block diagram shown in FIG. 2 when observation is impossible due to the target hidden behind mountains or some other obstruction.
First, the configuration of a conventional route predicting apparatus when a target is observable will be described with reference to FIG. 1. In FIG. 1, the route predicting apparatus comprises an observation unit 100 for observing a target and outputting an observed value y(k) thereof, and a prediction unit 200 coupled to receive the observed value y(k) for outputting signals x(k/k) and x(k+1/k) respectively indicative of an estimated state and a predicted state of the target. The observation unit 100 comprises a sensor (a radar or the like) 101 for observing a target and a data processor 102 for processing output signals from the sensor 101 to output the observed value y(k). The prediction unit 200 comprises a delay element 201 coupled to receive the predicted state signal x(k+1/k) for delaying the signal x(k+1/k) by a unit time to output a predicted state signal x(k/k-1). It is noted that the word "state" means information which includes the above-mentioned observed value, which merely indicates a position of a target, supplemented with a speed and an accelerated speed of the target. On the other hand, the above-mentioned observed value merely indicates information of an observed position of the target. A portion k/k- 1 in parenthesis in the predicted state signal indicates a predicted value of the state at a time k based on observed values which have been obtained by a time k-1. The prediction unit 200 further comprises an observation equation processing element 202 coupled to receive the predicted state signal x(k/k-1) for outputting a predicted observed value y(k/k-1), a first addition and subtraction element 203 for calculating a difference between the predicted observed value y(k/k-1) and the observed value y(k) to generate a difference signal v(k) which is referred to as an innovation process in the Kalman filter, a filter gain processing element 204 coupled to receive the innovation process v(k) for outputting a modifying signal, a second addition and subtraction element 205 for calculating a sum signal x(k/k) of the modifying signal and the predicted state signal, where the sum x(k/k) indicates an estimated state, and a system dynamics processing element 206 coupled to receive the estimated state signal for outputting a signal x(k+1/k) indicating a predicted state a unit time later, the predicted state signal being again input to the delay element 201 for use in processing which will be performed a unit time later.
FIG. 2 illustrates the configuration of the conventional route predicting apparatus when a target is not observable. Since no observed value is available, the prediction unit 200 only comprises the system dynamics processing element 206. In this configuration, the system dynamics processing element 206 is repetitively supplied with predicted state signals and extrapolates the predicted states. In FIG. 2, a portion "k+j+1/k" in parenthesis in the predicted state signal indicates a predicted value of the state at a time k+j+1 based on the observed values which have been obtained until the time k, "j" being incremented by one.
The operation of the above-mentioned prior art example will be described with reference to a flowchart of FIG. 3. First, at steps ST100 the data processor 102 determines whether or not a target is observable. If it is observable, the processing flow proceeds to step ST200 where the sensor observes the target, and the data processor 102 processes data output from the sensor 101 to output an observed value y(k). The configuration of the route predicting apparatus in this event is represented by the block diagram of FIG. 1. Then, a series of operations is performed in step ST300 for generating an estimated state and a predicted state of the target from the observed value y(k) in accordance with the Kalman filter. A series of equations relative to the Kalman filter is as follows: EQU x(k/k)=x(k/k-1)+K(k)[y(k)-Hx(k/k-1)] (1) EQU K(k)=P(k/k-1)H.sup.T [HP(k/k-1)H.sup.T +R].sup.-1 ( 2) EQU P(k/k)=[I-K(k)H]P(k/k-1) (3) EQU x(k+1/k)=.PHI.x(k/k) (4) EQU P(k+1/k)=.PHI.P(k/k).PHI..sup.T +Q (5)
where
x(k): a state of the target at a time k; PA1 x(i/j): a predicted state or an estimated state of x(i) at a time j; PA1 p(i/j): a covariance matrix of x(i/j); PA1 K(k): a gain at the time k; PA1 .PHI., H, I: a transition matrix, an observation matrix, and a unit matrix. PA1 Q, R: covariance matrices of system noise and observation noise PA1 observing means for outputting a route value representative of a route of a target; PA1 terrain information means for outputting characteristic parameters of prestored terrain information; and PA1 predicting means coupled to receive the route value and the characteristic parameters for predicting a route of the target when the target is observable, and coupled to receive the characteristic parameters and a predicted route successively for extrapolating the route when the target is not observable. PA1 first inferring means coupled to receive the route value, the characteristic parameters and a first predicted route value representing a predicted route of the target at the current time and which has been predicted a unit time prior to the current time for outputting a second predicted route value of the target a unit time later than the current time; and PA1 delay means for delaying the second predicted route value by a unit time to output the first predicted route value; and PA1 second inferring means coupled to successively receive the characteristic parameters and a predicted route value at intervals of unit time for outputting a predicted route value of the target a unit time later from each time. PA1 subtracting means coupled to receive the first predicted route value and the route value for outputting an error signal indicative of a difference therebetween; and PA1 learning means coupled to receive the error signal for learning route prediction to adjust the first inferring means so as to compensate for the error signal. PA1 observing means for observing a target to output an observed value representative of a route of the target; PA1 memory means for prestoring terrain information; PA1 calculating means responsive to the terrain information from the memory means and an estimated state of the target for calculating a steering amount of the target; and PA1 predicting means responsive to the observed value from the observing means and the steering amount from the calculating means for outputting a signal representative of an estimated state of the target and a signal representative of a predicted state of the target, the signal representing the estimated state of the target being fed to the calculating means. PA1 means responsive to the signal representing the predicted state of the target for outputting a predicted observed value; PA1 means responsive to the observed value and the predicted observed value for outputting the signal representative of the estimated state of the target; and PA1 means responsive to the signal representative of the estimated state of the target for outputting the signal representative of the predicted state. PA1 memory means for prestoring terrain information; PA1 calculating means responsive to the terrain information from the memory means and a predicted state of the target for calculating a steering amount of the target; and PA1 predicting means responsive to the steering amount from the calculating means for outputting a signal representative of a predicted state of the target, the signal representative of the predicted state of the target being fed to the calculating means. PA1 observing means for observing a target to output an observed value representative of a route of the target; PA1 memory means for prestoring terrain information; PA1 first predicting means responsive to the terrain information from the memory means and an estimated current state of the target for outputting a maneuver signal representative of a maneuver taken by the target for the purpose of avoiding collision to an obstacle; and PA1 second predicting means responsive to the observed value from the observing means and the maneuver signal from the first predicting means for outputting a signal representative of an estimated state of the target and a signal representative of a predicted state of the target, the signal representative of the estimated state of the target being fed to the first predicting means. PA1 means responsive to the signal representative of the predicted state of the target for outputting a predicted observed value; PA1 means responsive to the observed value and the predicted observed value for outputting the signal representative of the estimated state of the target; and PA1 means responsive to the signal representative of the estimated state of the target for outputting the signal representative of the predicted state.
At step ST301, the observation equation processing element 202 is supplied with a predicted state signal x(k/k-1) at the present time obtained from the delay element 201, and calculates and outputs a value of the second term in the blanket [] of the equation (1). This processing is performed to fetch information relating to the position of the target from the predicted values representing the position and speed of the target. This value will be referred to as a predicted observed value y(k/k-1). Next, at step ST302, the addition and subtraction element 203 receives the predicted observed value y(k/k-1) and the observed value y(k), and calculates and outputs a value of the term in the blanket [] of the equation (1). This value is referred to as an innovation process v(k) in the Kalman filter. Further, at step ST303 the filter gain processing element 204 calculates an optimal filter gain in accordance with the equations (2), (3) and (5), and calculates and outputs a value of the second term on the right side of the equation (1). This value acts as a modifying signal. Then, at step ST304, the addition and subtraction element 205 receives the modifying signal and the predicted state signal x(k/k-1), and calculates and outputs a value of x(k/k) of the equation (1) representing an estimated state. At step ST305, the estimated state x(k/k) is input to the system dynamics processing element 206. The processing flow proceeds to step ST306 where the system dynamics processing element 206 receives the estimated state signal x(k/k), calculates the equation (4), and outputs a signal indicative of a predicted state a unit time later. The estimated state signal and the predicted state signal are the outputs of the route predicting apparatus. Finally at step ST400, it is determined whether the operation has been completed or not. If the operation has not been completed, the processing flow again returns to step ST100 a unit time later and the same processing is repeated. In this event, at step ST306 a predicted state value predicting a state a unit time later from the current time is used a unit time later as a value indicative of a predicted state at the current time obtained from a predicted value a unit time before. Such a time shift is achieved by the delay element 201 in the block diagram of FIG. 1.
On the other hand, if it is determined at step ST100 that observation is impossible, the processing flow proceeds to step ST500 where the predicted state signal is input to the system dynamics processing element 206. The configuration of the route predicting apparatus in this event is represented by the block diagram of FIG. 2. At step ST306, the system dynamics processing element 206 repetitively receives the predicted state signals in place of the estimated state signal and performs calculations for extrapolating the predicted states. The predicted state signal is an output of the route predicting apparatus. The equation for calculating this predicted state signal is expressed as follows: EQU x(k+j+1/k)=.PHI.x(k+j/k) (6)
The conventional route predicting apparatus, constructed such as described above, can maintain route prediction by extrapolating predicted states if observation of a target is temporarily impossible. However, if such a condition persists, predicted values are repetitively made based on previous assumed values, thereby causing a problem that reliability in route prediction is reduced.